Chapter 34: Geometrical Optics Mirrors · 2017. 12. 23. · Sign convention: 1)f is positive for...

Phys 2435: Chap. 34, Pg 1

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MirrorsMirrors PlanePlane Spherical (convex or concave)Spherical (convex or concave)

LensesLenses The lens equationThe lens equation LensmakerLensmaker’’s s equationequation Combination of lensesCombination of lenses


Chapter 34: Geometrical OpticsChapter 34: Geometrical Optics


MirrorsMirrors

New Topic


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Looking in the mirrorLooking in the mirror

The image by a plane mirror is virtual, upright, equalsize, equal distance, and with left and right reversed.

How to find the image?Ray diagram (or ray tracing)

Click here for AP15.4 simulation


How to find an image?How to find an image? Trace rays from object to mirror to eye. Brain assumes that light travels in a straight line ! Extend rays back behind mirror to form image.

This is a “virtual”image since it doesnot actually exist behind the mirror.

The image by a plane mirroris virtual, upright, equal size,equal distance, and with leftand right reversed.


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Spherical MirrorsSpherical Mirrors

In general spherical mirrors do notfocus at a single point. (aberration)

Paraxial approximation (small angleapproximation): mirror is smallcompared to its radius of curvatureso a single focal point exists. Thefocal length is

f =r

2

(Parabolic mirrors do have a perfectfocus.)


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Concave Spherical Mirrors: image formationConcave Spherical Mirrors: image formation

If object is in betweencenter and focal point, theimage is real (light passesthough), inverted, andenlarged.


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Example: Ray TracingExample: Ray Tracing The object is placed beyond the center point. What is the

image?

C•

F•

The image is real, inverted, reduced.


Spherical Mirrors: calculationsSpherical Mirrors: calculations

Lateral magnification:

1

do+1

di=1

f

m =hi

ho

= !di

do

Mirror equation:

Sign conventions:hi is positive if upright, negative if inverted.do and di are positive if on the reflecting side, negative if onthe other side.


Summary: Concave MirrorsSummary: Concave Mirrors(assume f = 2 cm, then r = 4 cm)(assume f = 2 cm, then r = 4 cm)

Object: inside focal point (do=1.5 cm)Image: virtual, upright, enlarged

1

3+

1

di

=1

2, d

i= 6 cm

m = !6

3= !2

1

1.5+

1

di

=1

2, d

i= !6 cm

m = !!6

1.5= 4

Object: in between center and focal point (do=3 cm)Image: real, inverted, enlarged

1

6+

1

di

=1

2, d

i= 3 cm

m = !3

6= !0.5

Object: outside center point (do=6 cm)Image: real, inverted, reduced

1

do+1

di=1

f

m =hi

ho

= !di

do

Phys 2435: Chap. 34, Pg 10

Convex Spherical MirrorsConvex Spherical Mirrors

Magnification equationalso holds

1

do+1

di=1

f

m =hi

ho

= !di

do

Convex mirrors produce virtual,upright and smaller images.

Mirror equation stillholds, but f is negative.

For example, a convex rearview car mirror hascurvature r =16 m. The image of an object 10 maway from the mirror is

1

10+

1

di

=1

!8, so d

i= !4.4m

m = !di

do

= !!4.4

10= 0.44

Warning: objects in mirror may be closer than they appear.

Phys 2435: Chap. 33, Pg 11

Refraction at a spherical surfaceRefraction at a spherical surface

Equation also holds for concavesurface, but R is negative

n1

do

+n2

di

=n2! n

1

R

For example, A person looks vertically downinto a 1-m deep pool. How deep does thepool appear to be?

1.33

1.0+1

di

=1!1.33

"

di

= !0.75 m

Convex surface

Phys 2435: Chap. 33, Pg 12

ConcepTestConcepTest 34.1 34.1(Post) Plane mirrorPlane mirror1) towards you with v2) towards you with 2v3) away from you with v4) away from you with 2v

If you walk directlyIf you walk directlytowards a planetowards a planemirror at a speed mirror at a speed vv,,your image will moveyour image will move

Phys 2435: Chap. 33, Pg 13

LensesLenses

New Topic

Phys 2435: Chap. 33, Pg 14

Thin LensesThin Lenses

‘Thin’ in the sense that the thickness is much smaller than thediameter.

They form the basis of optical instruments: eyeglasses,cameras, telescopes, …

Phys 2435: Chap. 33, Pg 15

Thin LensesThin Lenses

Focal point, focal length, focal plane.

Optometrists like to use the reciprocal of the focus length,called power, P = 1/f. Unit is diopter (D). 1D = 1 m-1.For example, a 20-cm-focal-length converging lens has apower of P = 1/0.2 = 5.0 D. If it’s diverging, P = -5.0 D

Phys 2435: Chap. 33, Pg 16

Thin Lenses: Ray DiagramsThin Lenses: Ray Diagrams

Phys 2435: Chap. 33, Pg 17

The Lens EquationThe Lens Equation

1

do+1

di=1

f

m =hi

ho

= !di

do

Sign convention:1) f is positive for converging lens,

negative for diverging lens.2) do is positive if it is on the same side of

incident light, negative otherwise.3) di is positive if it is on the opposite side

of incident light, negative otherwise4) hi (or m) is positive if the image is upright

and negative if inverted, relative to theobject. (ho is always taken as positive)

Click here for thin lens simulation AP15.9

Phys 2435: Chap. 33, Pg 18

Example: What is the position and size of theExample: What is the position and size of theimage of a image of a 7.6-cm 7.6-cm high flower placed high flower placed 1 m1 m from a from a

+50-mm-focal-length+50-mm-focal-length camera lens? camera lens?

1

100+1

di

=1

5

m =hi

ho

= !di

do

= !5.26

100= !0.0526

di

= 5.26 cm

hi

= mho

= !0.0526 " 7.6 = !0.4 cm

Real, inverted, reduced

Phys 2435: Chap. 34, Pg 19

More Examples: Converging LensMore Examples: Converging Lens(assume f = 20 cm)(assume f = 20 cm)

Object: inside focal point (do=15 cm)Image: virtual, upright, enlarged

1

30+

1

di

=1

20, d

i= 60 cm

m = !60

30= !2

1

15+

1

di

=1

20, d

i= !60 cm

m = !!60

15= 4

Object: outside focal point (do=30 cm)Image: real, inverted, enlarged

1

60+

1

di

=1

20, d

i= 30 cm

m = !30

60= !0.5

Object: outside focal point (do=60 cm)Image: real, inverted, reduced

1

do+1

di=1

f

m =hi

ho

= !di

do

Phys 2435: Chap. 34, Pg 20

Combination of LensesCombination of Lenses

1

60+

1

di1

=1

20, d

i1= 30 cm

m1

= !di1

do1

= !30

60= !0.5

Basic idea: the image formed by the 1st lens is the object forthe 2nd lens, and so on. (Watch out for signs!)Example: f1=20 cm, f2=25 cm,object is placed 60 cm in front.

1

80 ! 30+

1

di2

=1

25, d

i2= 50 cm

m2

= !di2

do2

= !50

50= !1

m = m1m2 = (!0.5) " (!1) = 0.5

Phys 2435: Chap. 34, Pg 21

LensmakerLensmaker’’ss Equation Equation

Example: double-convex, n=1.52,absolute radius 10 cm for both surfaces,then the focal length is

1

f= (n !1)

1

R1

!1

R2

"

# $

%

& '

cm 6.9

10

1

10

1)152.1(

1

=

!"#

$%&

'''=

f

f

Symmetric in R1and R2 : so f is thesame both ways.

Example: double-concave, n=1.52,absolute radius 10 cm for both surfaces,

1

f= (1.52 !1)

1

!10!

1

10

" # $

% & '

f = !9.6 cm

Phys 2435: Chap. 34, Pg 22

ConcepTestConcepTest 34.2 34.2(Post) LensLens

• A light source is held near a lens and its light focuses at point B, asshown in the top figure. If the light source is moved closer to thelens, then at which of the indicated points will the light focus?

Chapter 34: Geometrical Optics Mirrors · 2017. 12. 23. · Sign convention: 1)f is positive for...

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